Find: the bulk modulus of elasticity of a body which experiences a change in pressure of \(5000\,Pa\) and a change in its volume from \(4.00\,cm^{3}\) to \(3.90\,cm^{3}\).
A sphere of radius \(10\,mm\) is compressed to its half of original volume by applying an external force of \(100\,N\). Fund: the bulk modulus of the sphere.
Find: the decrease in volume of \(3\,litres\) of water if it is subjected to a pressure of \(\left(1.0\times10^{10}\right)Pa\). Compare it with the decrease in volume of mercury under the same pressure. Bulk Modulii of water and the Mercury are \(\left(2.2\times10^{9}\right)\frac{N}{m^{2}}\) and \(\left(2.5\times10^{10}\right)\frac{N}{m^{2}}\) respectively.
The average depth of Indian ocean is \(3\,Km\). Calculate: the fractional compression \(\frac{\Delta V}{V}\) of water at the bottom of the ocean. Given: that the bulk modulus of water \(\left(2.2\times10^{9}\right)\frac{N}{m^{2}}\). Take: \(g=9.8\frac{m}{s^{2}}\).
Ans: \(\%\frac{\Delta V}{V}=1.36\%\).
When the water freezes, it expands about \(9\%\). What pressure increase would occur inside an auto mobile engine if the water freezes? The bulk Modulus of Water \(\left(2\times10^{9}\right)\frac{N}{m^{2}}\).
Ans: \(p=\left(1.65\times10^{8}\right)Pa\).
A pressure of \(20\,atm\) is applied on \(10^{4}\,cm^{3}\) of water. Find: the \(\%\) change in volume of water. Given; the compressibility of water \(=\left(5\times10^{-10}\right)\frac{N}{m^{2}}\), density of mercury \(=13600\frac{Kg}{m^{3}}\), \(g=9.8\frac{m}{s^{2}}\) and \(1\,atm=76\,cm\,of\,mercury\).
Ans: \(\frac{\Delta V}{V}\times100\%=0.101\%\).
When a solid rubber ball is subjected to a uniform stress of \(1.0\times10^{4}\frac{N}{m^{2}}\), Its volume is reduced by \(10\%\). Find: the bulk Modulus of for rubber.
A solid brass sphere of volume \(0.1\,m^{2}\) is brought in the deep sea water. If, the pressure on the brass sphere is \(\left(2\times10^{8}\right)\frac{N}{m^{2}}\). Find: the change in volume of the sphere. Bulk Modulus of Elasticity of water is \(\left(6\times10^{10}\right)\frac{N}{m^{2}}\).
Density of sea water at the surface is \(1.03\frac{g}{cm^{-3}}\). What is its density at a depth where the pressure is \(\left(1.01\times10^{8}\right)\frac{N}{m^{2}}\)?Bulk Modulus of Water is \(\left(2.2\times10^{9}\right)\frac{N}{m^{2}}\).
Ans: \(\rho=1.077\frac{g}{cm^{3}}\).
The fractional compression of water in the ocean at a certain depth is \(1.36\%\). If, the bulk modulus of elasticity of water is \(\left(2.2\times10^{9}\right)\frac{N}{m^{2}}\). Find: the depth of ocean at the place. Given: Density of Water in the ocean \(=\left(1.03\times10^{3}\right)\frac{kg}{m^{3}}\) and \(g=9.8\frac{m}{s^{2}}\).
Ans: \(Depth=2964\,m\).
The density of aluminium at \(1\,atm\) pressure is \(\left(2.710\times10^{3}\right)\frac{kg}{m^{3}}\). Find: the density when subjected to a pressure of \(1975\times 1\,atm\). Compressibility of aluminium is \(\left(1.389\times10^{-11}\right)Pa^{-1}\). \left[Take: 1\,atm=\left(1.013\times10^{5}\right)Pa\right].
The each side of the solid cube is shortened by \(1\%\) when subjected to an additional pressure of \(\left(5\times10^{5}\right)\frac{N}{m^{2}}\). Find:(a) Volumetric Strain. (b) Compressibility of the material of the cube.
Ans:(a) \(\frac{\Delta V}{V}=0.03\) and (b) \(\beta=\left(6\times10^{-8}\right)Pa^{-1}\).
A solid sphere of radius \(R\) made of a material of bulk modulus of elasticity \(\left(1.0\times10^{6}\right)\frac{N}{m^{2}}\) is surrounded by a liquid in a cylindrical container. A massless piston of cross-sectional area \(10^{-2}\,m^{2}\) floats on the surface of the liquid. When a mass of \(100\,kg\) is placed on the piston to compress the liquid. Find: The fractional change in radius of the sphere?
